Speaker: Hsin-Yi Yang，University of Amsterdam

Title: CM-liftability of simple superspecial abelian surfaces over \F_{p}

Language: English

Time & Venue: 2026.07.15 15:15-16:15 MCM110

Abstract: In 1992, Oort asked a question: Does there exist a CM lifting of an abelian variety over a field with characteristic p>0?

The CM-liftability of ordinary simple abelian surfaces is proved by Serre-Tate, and the CM-liftability of almost ordinary simple abelian surfaces is proved by Oswal-Shankar and Bergström-Karemaker-Marseglia, respectively.

Our work shows the CM-liftability of simple superspecial abelian surfaces over \F_{p} by using the so-called residual reflex condition and Lie types. As there can only be ordinary, almost ordinary, or supersingular simple abelian surfaces over \F_{p}, our work is another step to complete the CM-liftability of simple abelian surfaces over \F_{p}.

In this talk, we will explain the main idea of the proof by an example: a simple superspecial abelian surface over \F_{7} in the isogeny class, which is determined by the Weil-7 number \sqrt{7}\zeta_{3}.